2011/12/14 by Nobuhiro Honda, Honda, Nobuhiro
Mathematics · #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #math.AG #math.DG
paper · pdf · doi:10.48550/arxiv.1112.3109
51 pages, 6 figures. This is a combination of the author's three articles arXiv:1009.3153, 1108.1443, and 1109.5427, minus some detailed construction of the twistor spaces
arxiv created 2011/12/14 · arxiv updated 2011/12/15
In this paper we classify all Moishezon twistor spaces on 4CP2. The classification is given in terms of the structure of the anticanonical system of the twistor spaces. We show that the anticanonical map satisfies one of the following three properties: (a) birational over the image, (b) two to one over the image, or (c) the image is two-dimensional. We determine structure of the images for each case in explicit forms. Then we intensively investigate structure of the twistor spaces in the case (b), and determine the defining equation of the branch divisor of the anticanonical map.